Seems to work in Wine in Linux. I didn't try to actually play any games, but I was able to enter game rooms for Hearts and Spades.
What I did:
1. Install winetricks firefox
2. Go to the safeharborgames website and download the installer (you can do this in any browser)
3. the installer is an msi file, so install it with msiexec /i
4. Using Firefox in Wine, go to the safeharborgames website
5. Create an account if you haven't already, and log in
6. Click on whatever game you want to play
7. When prompted to install flash player, accept.
8. Click on whatever room you want to enter
9. When prompted for what application to launch with, click the Choose button, browse to the directory where harborgames.exe is located, and choose that. The first time you do that, it will download the games.
10. Wait for the game to load. It takes about 20 seconds.
I'm not a card player, so someone else will have to test whether actually playing the games works.
Note that the desktop link for safeharborgames doesn't work, but running Firefox and going to the website does.
As for the "access denied" when trying to install, that sounds like a permissions issue.